新四维耗散非线性系统动力学行为分析及电路设计  

Dynamic Behavior Analysis of a Novel Four-Dimensional Dissipative Nonlinear System with Its Circuit Design

作　　者：瞿民凯 汤琼[1] 赵思远 黄驿婷 罗芳文 QU Minkai;TANG Qiong;ZHAO Siyuan;HUANG Yiting;LUO Fangwen(College of Science,Hunan University of Technology,Zhuzhou Hunan 412007,China)

机构地区：[1]湖南工业大学理学院,湖南株洲412007

出　　处：《湖南工业大学学报》2023年第5期17-27,共11页Journal of Hunan University of Technology

基　　金：湖南省自然科学基金资助项目(2023JJ50164)。

摘　　要：在三维混沌系统的基础上,通过非线性反馈控制,构造了一个新的四维超混沌系统。分析了该系统平衡点的稳定性,运用相图、分岔图、Lyapunov指数谱、庞加莱截面图等方法,对系统随参数变化呈周期、混沌、超混沌状态的动力学行为进行了分析。分别利用有限元方法和Runge-Kutta方法求得该系统的数值解,并进行了对比。最后设计了该系统的模拟电路,验证了该系统的可实现性。On the basis of the three-dimensional chaotic system,a new four-dimensional hyperchaotic system is constructed through nonlinear feedback control.An analysis has been made of the stability of the equilibrium point of the system,followed by a further analysis of the dynamic behavior of the system in periodic,chaotic and hyperchaotic states with parameter changes by using phase diagram,bifurcation diagram,Lyapunov exponential spectrum,Poincarécross-sectional diagram as well as other methods.The numerical solutions of the system can be obtained by adopting finite element method and Runge-Kutta method respectively,accompanied by a comparison between them.Finally,the feasibility of the system can be verified with the designed system analog circuit.

关 键 词：超混沌系统 分岔图 LYAPUNOV指数谱 有限元方法 电路实现 

分 类 号：O175[理学—数学]